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Introduction To Algebraic Coding Theory

2022-02-18 Mathematics
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Release : 2022-02-18
Genre : Mathematics
Kind : eBook
Book Rating : 980/5 ( reviews)

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Book Synopsis Introduction To Algebraic Coding Theory by : Tzuong-tsieng Moh

Download or read book Introduction To Algebraic Coding Theory written by Tzuong-tsieng Moh. This book was released on 2022-02-18. Available in PDF, EPUB and Kindle. Book excerpt: In this age of technology where messages are transmitted in sequences of 0's and 1's through space, errors can occur due to noisy channels. Thus, self-correcting code is vital to eradicate these errors when the number of errors is small. It is widely used in industry for a variety of applications including e-mail, telephone, and remote sensing (for example, photographs of Mars).An expert in algebra and algebraic geometry, Tzuong-Tsieng Moh covers many essential aspects of algebraic coding theory in this book, such as elementary algebraic coding theories, the mathematical theory of vector spaces and linear algebras behind them, various rings and associated coding theories, a fast decoding method, useful parts of algebraic geometry and geometric coding theories.This book is accessible to advanced undergraduate students, graduate students, coding theorists and algebraic geometers.

Algebraic Coding Theory (Revised Edition)

2015-03-26 Mathematics
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Release : 2015-03-26
Genre : Mathematics
Kind : eBook
Book Rating : 91X/5 ( reviews)

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Book Synopsis Algebraic Coding Theory (Revised Edition) by : Elwyn R Berlekamp

Download or read book Algebraic Coding Theory (Revised Edition) written by Elwyn R Berlekamp. This book was released on 2015-03-26. Available in PDF, EPUB and Kindle. Book excerpt: This is the revised edition of Berlekamp's famous book, 'Algebraic Coding Theory', originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering practice in this field. One of these is an algorithm for decoding Reed-Solomon and Bose-Chaudhuri-Hocquenghem codes that subsequently became known as the Berlekamp-Massey Algorithm. Another is the Berlekamp algorithm for factoring polynomials over finite fields, whose later extensions and embellishments became widely used in symbolic manipulation systems. Other novel algorithms improved the basic methods for doing various arithmetic operations in finite fields of characteristic two. Other major research contributions in this book included a new class of Lee metric codes, and precise asymptotic results on the number of information symbols in long binary BCH codes.Selected chapters of the book became a standard graduate textbook.Both practicing engineers and scholars will find this book to be of great value.

Introduction to Coding Theory

2013-03-09 Mathematics
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Release : 2013-03-09
Genre : Mathematics
Kind : eBook
Book Rating : 984/5 ( reviews)

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Book Synopsis Introduction to Coding Theory by : J. H. van Lint

Download or read book Introduction to Coding Theory written by J. H. van Lint. This book was released on 2013-03-09. Available in PDF, EPUB and Kindle. Book excerpt: Coding theory is still a young subject. One can safely say that it was born in 1948. It is not surprising that it has not yet become a fixed topic in the curriculum of most universities. On the other hand, it is obvious that discrete mathematics is rapidly growing in importance. The growing need for mathe maticians and computer scientists in industry will lead to an increase in courses offered in the area of discrete mathematics. One of the most suitable and fascinating is, indeed, coding theory. So, it is not surprising that one more book on this subject now appears. However, a little more justification of the book are necessary. A few years ago it was and a little more history remarked at a meeting on coding theory that there was no book available an introductory course on coding theory (mainly which could be used for for mathematicians but also for students in engineering or computer science). The best known textbooks were either too old, too big, too technical, too much for specialists, etc. The final remark was that my Springer Lecture Notes (# 201) were slightly obsolete and out of print. Without realizing what I was getting into I announced that the statement was not true and proved this by showing several participants the book Inleiding in de Coderingstheorie, a little book based on the syllabus of a course given at the Mathematical Centre in Amsterdam in 1975 (M. C. Syllabus 31).

Introduction to Coding Theory

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 752/5 ( reviews)

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Book Synopsis Introduction to Coding Theory by : J.H. van Lint

Download or read book Introduction to Coding Theory written by J.H. van Lint. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: It is gratifying that this textbook is still sufficiently popular to warrant a third edition. I have used the opportunity to improve and enlarge the book. When the second edition was prepared, only two pages on algebraic geometry codes were added. These have now been removed and replaced by a relatively long chapter on this subject. Although it is still only an introduction, the chapter requires more mathematical background of the reader than the remainder of this book. One of the very interesting recent developments concerns binary codes defined by using codes over the alphabet 7l.4• There is so much interest in this area that a chapter on the essentials was added. Knowledge of this chapter will allow the reader to study recent literature on 7l. -codes. 4 Furthermore, some material has been added that appeared in my Springer Lec ture Notes 201, but was not included in earlier editions of this book, e. g. Generalized Reed-Solomon Codes and Generalized Reed-Muller Codes. In Chapter 2, a section on "Coding Gain" ( the engineer's justification for using error-correcting codes) was added. For the author, preparing this third edition was a most welcome return to mathematics after seven years of administration. For valuable discussions on the new material, I thank C.P.l.M.Baggen, I. M.Duursma, H.D.L.Hollmann, H. C. A. van Tilborg, and R. M. Wilson. A special word of thanks to R. A. Pellikaan for his assistance with Chapter 10.

Elements of Algebraic Coding Theory

1996-07-01 Mathematics
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Release : 1996-07-01
Genre : Mathematics
Kind : eBook
Book Rating : 804/5 ( reviews)

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Book Synopsis Elements of Algebraic Coding Theory by : L.R. Vermani

Download or read book Elements of Algebraic Coding Theory written by L.R. Vermani. This book was released on 1996-07-01. Available in PDF, EPUB and Kindle. Book excerpt: Coding theory came into existence in the late 1940's and is concerned with devising efficient encoding and decoding procedures. The book is intended as a principal text for first courses in coding and algebraic coding theory, and is aimed at advanced undergraduates and recent graduates as both a course and self-study text. BCH and cyclic, Group codes, Hamming codes, polynomial as well as many other codes are introduced in this textbook. Incorporating numerous worked examples and complete logical proofs, it is an ideal introduction to the fundamental of algebraic coding.

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